# Compact Flourescent Lightbulb Efficiency

Compact Fluorescent Lightbulbs (CFLs) are quite the rage in home lighting these days. I've replaced most of the bulbs in my house with CFLs. Let us examine the energy and financial efficiencies of these bulbs.

## Energy Efficiencies

The input of lightbulbs is their power consumption. Power consumption is measured in Watts. The output of lightbulbs is how bright it is. Brightness is measured in lumens.

The most common type of CFL is the 13 watt lightbulb. It is the replacement for the common 60 Watt incandescent bulb. Table 1 shows relevant inputs and outputs for these two bulbs.

Input Power (Watt) Output Light (Lumen) Luminous Efficacy (Lumen/Watt)
Incandescent 60 850 850/60 ≅ 14.16
Compact Fluorescent 13 900 900/13 ≅ 69.23

CFLs have a higher lumen output and a lower watt input resulting in almost 5 times greater efficacy. Note though, that I don't say efficiency. Efficiency is a dimensionless quantity, and Lumen/Watt is not dimensionless. If you had a lightbulb that gave off 1000 Lumens at 9 Watts. You would compute its luminous efficacy to be 111 (1000/9). 111 is greater than the maximum energy efficiency you could have (100%). If your lightbulb is greater than 100% efficient it would mean that it actually created energy out of nowhere.

To compute a bulbs efficiency we need the theoretical maximum luminous efficacy. The theoretical maximum represents a lightbulb that turned all of its power into visible light photons. The theoretical maximum luminous efficacy is 683.002 Lumen/Watt. Give this, the luminous efficiency is given by the luminous efficacy divided by the maximum efficacy. The results of this computation are seen in Table 2.

Luminous Efficiency
Incandescent 14.16/683.002 ≅ 2%
Compact Fluorescent 69.23/683.002 ≅ 10%

So in the case of CFLs 10% of the power consumed is being converted into light. Ideally we want 100% of the energy to be converted into light, but 10% is 5 times better than the incandescent bulbs at 2%.

If we swap incandescents for the more efficient CFLs we will realize a significant energy savings. Incandescents use 60 watts and CFLs use 13 watts. The difference is 47 watts. If we take that over the useful life of a CFL bulb, 10,000 hours, we get 470 kW hours of savings. At a usage rate of 3 hours per day, you can use 51.5 kW hours fewer a year.

From an energy perspective, CFLs represent a significant improvement over prior bulbs. Energy savings alone is not a reason to do something though. If CFLs cost $500 per bulb you would not want to pay for one. Let's see if we can really afford these bulbs. ## Financial Efficiencies To decide whether to invest in CFLs we need to decide if the Net Present Value (NPV) of the bulb switch investment is positive. To upgrade the bulbs capital must be invested. Since you have to have at least one kind of bulb the capital invested is the difference in price between a CFL bulb ($2.74) and a incandescent bulb ($0.36). This investment yields two distinct returns. The first is the energy savings. If we assume an energy cost of 10 cents per kilowatt hour, the switch saves 43 cents each month. The second is replacement savings. Incandescent bulbs are rated for 1000 hours of use and CFLs are rated for 10,000 hours of use. Each year we forgo the replacement cost of an incandescent bulb. Since cash in the future is not as good as cash now (cash now can be invested in other things) we must use NPV to calculate how much this is worth to us. The NPV calculation discounts cash returns in the future. The rate of discount is based on some rate of return we think we can get doing something else. For instance, at the time of writing the US 10 year bond is at 3.83%. So if you invested your capital in a US bond instead of a lightbulb would you come out ahead? That's what we aim to ask by using NPV. It turns out that the NPV for the CFL investment is$44.73. Since this number is positive, it means that investing in CFLs is a good option compared to investing in US Bonds.

It is useful to look at your break even point. Say you are only living in a place for a short time. If you move before the break even point you will have wasted cash buying CFLs. If you move after the break-even point, the CFLs will be worth it to you. The break even point is the time when the Net Present Value first becomes positive. In this case, the break even point for the CFL investment is at 8 months. At 8 months, you will have recouped your investment and made 17 cents.

Another useful number is your return on investment. The capital outlay is $2.37 and the total return is$57.42. The return on investment is 2422% over 9 years.

CFLs appear to be a good investment vehicle for people looking to earn great returns on their capital. Unfortunately it does not scale well. Once you have invested capital in all of your lightbulbs you cannot continue to achieve such large returns on investment.